Discretized fractional calculus
SIAM Journal on Mathematical Analysis
Wave field simulation for heterogeneous porous media with singular memory drag force
Journal of Computational Physics
Numerical modeling of 1D transient poroelastic waves in the low-frequency range
Journal of Computational and Applied Mathematics
Efficient solution of a wave equation with fractional-order dissipative terms
Journal of Computational and Applied Mathematics
Time domain numerical modeling of wave propagation in 2D heterogeneous porous media
Journal of Computational Physics
Numerical modeling of transient two-dimensional viscoelastic waves
Journal of Computational Physics
Numerical modeling of nonlinear acoustic waves in a tube connected with Helmholtz resonators
Journal of Computational Physics
Hi-index | 31.45 |
A time-domain numerical modeling of Biot poroelastic waves is presented. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by Johnson-Koplik-Dashen (JKD). Some of the coefficients in the Biot-JKD model are proportional to the square root of the frequency: in the time-domain, these coefficients introduce order 1/2 shifted fractional derivatives involving a convolution product. Based on a diffusive representation, the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. Thanks to the dispersion relation, the coefficients in the diffusive representation are obtained by performing an optimization procedure in the frequency range of interest. A splitting strategy is then applied numerically: the propagative part of Biot-JKD equations is discretized using a fourth-order ADER scheme on a Cartesian grid, whereas the diffusive part is solved exactly. Comparisons with analytical solutions show the efficiency and the accuracy of this approach.